2021/06/25 by Leyffer, Sven, Manns, Paul · 2 citations
#49M05 #90C10 #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2106.13453
We propose a trust-region method that solves a sequence of linear integer programs to tackle integer optimal control problems regularized with a total variation penalty. The total variation penalty allows us to prove the existence of minimizers of the integer optimal control problem. We introduce a local optimality concept for the problem, which arises from the infinite-dimensional perspective. In the case of a one-dimensional domain of the control function, we prove convergence of the iterates produced by our algorithm to points that satisfy first-order stationarity conditions for local optimality. We demonstrate the theoretical findings on a computational example.